Here you have a few options to choose from
http://www.timeout.com/london/featur...ts-in-december
The wife will probably enjoy the Real food Christmas market and Walking around the main atractions in the evening to see Christmas lights.
Iceskating and warm drinks one afternoon
http://www.viewlondon.co.uk/whatson/...ature-495.html
Date night at a nice restaurant followed by cocktails sounds like something you would enjoy and maybe if you your budget allows, perhaps go to a show...
http://www.londontheatre.co.uk/londo...ndcalendar.htm
and if anything else fails just get piss-drunk like all the locals do to deal with the cold ;)